{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Frequency-Domain Linear Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "此示例演示如何使用numpy库中的离散傅里叶变换为时间序列构造线性回归模型。此示例中使用的时间序列是 1973 年至 1979 年美国每月意外死亡人数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "数据如下，需要注意的是如果想要使用numpy中的fft，需要将numpy的矩阵设定为复数形式，否则可能会出错。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ts= np.array( [9007.+0j,8106.+0j,8928.+0j,9137.+0j,10017.+0j,10826.+0j,11317.+0j,10744.+0j,9713.+0j,9938.+0j,9161.+0j,8927.+0j,\n",
    "                7750.+0j,6981.+0j,8038.+0j,8422.+0j,8714.+0j,9512.+0j,10120.+0j,9823.+0j,8743.+0j,9129.+0j,8710.+0j,8680.+0j,\n",
    "                8162.+0j,7306.+0j,8124.+0j,7870.+0j,9387.+0j,9556.+0j,10093.+0j,9620.+0j,8285.+0j,8433.+0j,8160.+0j,8034.+0j,\n",
    "                7717.+0j,7461.+0j,7776.+0j,7925.+0j,8634.+0j,8945.+0j,10078.+0j,9179.+0j,8037.+0j,8488.+0j,7874.+0j,8647.+0j,\n",
    "                7792.+0j,6957.+0j,7726.+0j,8106.+0j,8890.+0j,9299.+0j,10625.+0j,9302.+0j,8314.+0j,8850.+0j,8265.+0j,8796.+0j,\n",
    "                7836.+0j,6892.+0j,7791.+0j,8129.+0j,9115.+0j,9434.+0j,10484.+0j,9827.+0j,9110.+0j,9070.+0j,8633.+0j,9240.+0j])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "exdata是一个 12 x 6 的矩阵。的每一列包含 12 个月的数据。每列的第一行包含相应年份 1 月的美国意外死亡人数。每列的最后一行包含相应年份 12 月的美国意外死亡人数。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "将数据矩阵重塑为 72 x 1 的时间序列，并绘制 1973 年至 1978 年的数据。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of Accidental Deaths')"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "years = np.linspace(1973,1979,72)\n",
    "plt.plot(years,np.real(ts))\n",
    "plt.plot(years,np.real(ts),'o')\n",
    "plt.xlabel('Year')\n",
    "plt.ylabel('Number of Accidental Deaths')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "对数据的目视检查表明，意外死亡人数会定期变化，震荡周期似乎为一年，数据的周期性表明，一个合理的模型可能是：<br/>\n",
    "$X(n)=\\mu + \\sum\\limits_k(A_k cos(2\\pi kn/N)+B_kcos(2\\pi kn/N))+\\delta (n)$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "μ是整体均值，N是时间序列的长度，并且δ（n)是独立且同分布 （IID） 高斯随机变量的白噪声序列，均值为零，存在一些方差。加性噪声项解释了数据固有的随机性。模型的参数是余弦和正弦的总体均值和振幅。模型在参数中是线性的。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "要在时域中构建线性回归模型，必须指定余弦和正弦的频率，形成设计矩阵，并求解正态方程，以获得模型参数的最小二乘估计值。在这种情况下，使用离散傅里叶变换来检测周期性，仅保留傅里叶系数的子集，并反转变换以获得拟合的时间序列会更容易。\n",
    "\n",
    "对数据执行频谱分析，以揭示哪些频率对数据中的可变性有显著贡献。由于信号的总均值约为 9，000，并且与 0 频率下的傅里叶变换成正比，因此在频谱分析之前减去均值。这降低了0频率下较大的傅里叶系数，并使任何显着的振荡更容易检测。傅里叶变换中的频率以时间序列长度 1/72 的倒数间隔间隔。每月对数据进行采样，光谱分析中的最高频率为1个周期/2个月。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(72,)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "Text(0.5, 0, 'Cycles/Year')"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 720x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tsdft = np.fft.fft(ts-np.mean(ts))\n",
    "print(tsdft.shape)\n",
    "freq = np.linspace(0,0.5,37)\n",
    "plt.figure(figsize=(10,4))\n",
    "plt.plot(freq*12,np.abs(tsdft[0:int(len(ts)/2)+1]))\n",
    "plt.plot(freq*12,np.abs(tsdft[0:int(len(ts)/2)+1]),'o')\n",
    "plt.ylabel(\"Magnitude\")\n",
    "plt.xlabel(\"Cycles/Year\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "根据幅度，1周期/12个月的频率是数据中最重要的振荡。1周期/12个月的星等是任何其他星等的两倍多。然而，光谱分析显示，数据中还有其他周期性成分。例如，在 1 周期/12 个月的谐波（整数倍）处似乎存在周期性分量。似乎还有一个周期性成分，周期为1个周期/ 72个月。\n",
    "\n",
    "根据数据的频谱分析，使用余弦和正弦项拟合简单的线性回归模型，其频率为最重要的分量：1 周期/年（1 周期/12 个月）。\n",
    "\n",
    "确定离散傅里叶变换中对应于 1 个周期/12 个月的频率箱。由于频率间隔为 1/72，并且第一个 bin 对应于 0 频率，因此正确的 bin 是 72/12+1。这是正频率的频率箱。您还必须包括与负频率相对应的频率箱：-1 周期/12 个月。使用 MATLAB 分度时，负频率的频率箱为 72-72/12+1。\n",
    "\n",
    "创建一个 72 x 1 的零向量。用对应于 1 个周期/12 个月的正负频率的傅里叶系数填充矢量的相应元素。反转傅里叶变换并添加总体均值以获得与意外死亡数据的拟合。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, 72)\n"
     ]
    }
   ],
   "source": [
    "tsfit = np.zeros([72,1],dtype = complex)\n",
    "tsfit[6] = tsdft[6]\n",
    "tsfit[66] = tsdft[66]\n",
    "tsfit = np.array(tsfit.transpose())\n",
    "print(tsfit.shape)\n",
    "tsfit = np.fft.ifft(np.round(tsfit,0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用两个傅里叶系数绘制原始数据和拟合序列。\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of Accidental Deaths')"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "mu = np.mean(ts)\n",
    "tsfitt = mu+tsfit\n",
    "plt.plot(years,np.real(tsfitt).transpose())\n",
    "plt.plot(years,np.real(ts),'b')\n",
    "plt.plot(years,np.real(ts),marker = 'o')\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"Number of Accidental Deaths\")\n",
    "#plt.scatter(years, np.real(ts), color='', marker='o', edgecolors='g', s=200) # 把 corlor 设置为空，通过edgecolors来控制颜色"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def xcorr(x,y,timelaggy):\n",
    "    x = x.flatten()\n",
    "    y = y.flatten()\n",
    "    out = np.correlate(x,y,'full')\n",
    "    midIndex = int(len(out)/2)\n",
    "    mid = out[midIndex]\n",
    "    autocor = out/mid\n",
    "    if timelaggy>len(out)/2:\n",
    "        autocor = autocor\n",
    "        lags = np.linspace(-len(out)/2,len(out)/2,2*len(out)+1  )\n",
    "    else :\n",
    "        autocor = autocor[midIndex-timelaggy:midIndex+timelaggy+1]\n",
    "        lags = np.linspace(-timelaggy,timelaggy,2*timelaggy+1)\n",
    "    return autocor,lags"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "拟合模型似乎捕获了数据的一般周期性，并支持数据以1年的周期振荡的初步结论。\n",
    "\n",
    "要评估 1 个周期/12 个月的单一频率对观测时间序列的充分程度，请形成残差。如果残差类似于白噪声序列，则具有一个频率的简单线性模型已对时间序列进行了充分的建模。\n",
    "\n",
    "要评估残差，请使用白噪声具有 95% 置信区间的自相关序列。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Autocorrelation of Residuals')"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "resid = ts - tsfitt\n",
    "resid = np.real(resid)\n",
    "xc,lags = xcorr(resid,resid,50)\n",
    "plt.stem(lags[50:len(lags)],xc[50:len(xc)])\n",
    "lconf = -1.96*np.ones([51,1])/np.math.sqrt(72)\n",
    "uconf = 1.96*np.ones([51,1])/np.math.sqrt(72)\n",
    "plt.plot(lconf)\n",
    "plt.plot(uconf)\n",
    "plt.xlabel('Lag')\n",
    "plt.ylabel('Correlation Coefficient')\n",
    "plt.title('Autocorrelation of Residuals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "自相关值在多个滞后处落在 95% 置信区界之外。残差似乎不是白噪声。结论是，具有一个正弦分量的简单线性模型不能解释意外死亡次数中的所有振荡。这是可以预料的，因为光谱分析揭示了除了主要振荡之外的其他周期性成分。创建包含光谱分析所指示的其他周期项的模型将改善拟合并美白残差。\n",
    "\n",
    "拟合由三个最大傅里叶系数大小组成的模型。由于必须保留对应于负频率和正频率的傅里叶系数，因此请保留最大的 6 个指数。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(72,)\n",
      "(72,)\n"
     ]
    }
   ],
   "source": [
    "tsfit2dft = np.zeros([72],dtype=complex)\n",
    "print(tsfit2dft.shape)\n",
    "print(tsdft.shape)\n",
    "I = np.argsort(np.abs(tsdft))\n",
    "I = np.flipud(I)\n",
    "I = I[0:6]\n",
    "for i in I:\n",
    "    tsfit2dft[i] = tsdft[i]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "证明仅保留72个傅里叶系数（3个频率）中的6个可以保留大部分信号能量。首先，证明保留所有傅里叶系数会产生原始信号和傅里叶变换之间的能量等价性。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999999999"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(1/np.math.sqrt(72)*tsdft,2)/np.linalg.norm(ts-np.mean(ts),2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "该比率为 1。现在，检查仅保留 3 个频率的能量比。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8990884437844658"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.linalg.norm(1/np.math.sqrt(72)*tsfit2dft,2)/np.linalg.norm(ts-np.mean(ts),2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "几乎90%的能量被保留下来。等价地，时间序列方差的90%由3个频率分量占。\n",
    "\n",
    "根据 3 个频率分量形成数据估计值。比较原始数据、具有一个频率的模型和具有 3 个频率的模型。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Number of Accidental Deaths')"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "tsfit2 = mu + np.fft.ifft(tsfit2dft)\n",
    "plt.plot(years,np.real(ts),'b')\n",
    "plt.plot(years,np.real(ts),marker = 'o',color = 'blue')\n",
    "plt.plot(years,np.real(tsfitt).transpose(),color = 'red')\n",
    "plt.plot(years,np.real(tsfit2),color = 'orange')\n",
    "plt.xlabel(\"Year\")\n",
    "plt.ylabel(\"Number of Accidental Deaths\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用3个频率提高了与原始信号的拟合度。您可以通过检查 3 频模型中残差的自相关来查看这一点。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Autocorrelation of Residuals')"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "resid = ts - tsfit2\n",
    "resid = np.real(resid)\n",
    "xc,lags = xcorr(resid,resid,50)\n",
    "plt.stem(lags[50:len(lags)],xc[50:len(xc)])\n",
    "lconf = -1.96*np.ones([51,1])/np.math.sqrt(72)\n",
    "uconf = 1.96*np.ones([51,1])/np.math.sqrt(72)\n",
    "plt.plot(lconf)\n",
    "plt.plot(uconf)\n",
    "plt.xlabel('Lag')\n",
    "plt.ylabel('Correlation Coefficient')\n",
    "plt.title('Autocorrelation of Residuals')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用3个频率导致残差更接近白噪声过程。\n",
    "\n",
    "证明从傅里叶变换获得的参数值等效于时域线性回归模型。通过形成设计矩阵并求解法线方程，找到三个频率的总体均值、余弦幅度和正弦幅度的最小二乘估计值。将拟合时间序列与从傅里叶变换获得的时间序列进行比较。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "X = np.zeros([72,7])\n",
    "X[:,0] = 1\n",
    "X[:,1] = np.cos(2*np.pi/72*np.linspace(0,71,72)).transpose()\n",
    "X[:,2] = np.sin(2*np.pi/72*np.linspace(0,71,72)).transpose()\n",
    "X[:,3] = np.cos(2*np.pi*6/72*np.linspace(0,71,72)).transpose()\n",
    "X[:,4] = np.sin(2*np.pi*6/72*np.linspace(0,71,72)).transpose()\n",
    "X[:,5] = np.cos(2*np.pi*12/72*np.linspace(0,71,72)).transpose()\n",
    "X[:,6] = np.sin(2*np.pi*12/72*np.linspace(0,71,72)).transpose()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(72, 7)\n",
      "(72, 1)\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "D:\\anaconda\\envs\\pytorch\\lib\\site-packages\\ipykernel_launcher.py:7: FutureWarning: `rcond` parameter will change to the default of machine precision times ``max(M, N)`` where M and N are the input matrix dimensions.\n",
      "To use the future default and silence this warning we advise to pass `rcond=None`, to keep using the old, explicitly pass `rcond=-1`.\n",
      "  import sys\n"
     ]
    }
   ],
   "source": [
    "print(X.shape)\n",
    "ts2 = np.zeros([72,1])\n",
    "for i in range(len(ts)):\n",
    "    ts2[i,0] = np.real(ts[i])\n",
    "#ts = np.array(ts)\n",
    "print(ts2.shape)\n",
    "beta = np.linalg.lstsq(X,ts2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "bete = np.array(beta[0])\n",
    "bete.shape\n",
    "tsfit_lm = X.dot(bete)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1.2732925824820995e-11\n"
     ]
    }
   ],
   "source": [
    "# print(tsfit_lm.shape)\n",
    "# print(tsfit2.shape)\n",
    "aa = np.abs(tsfit_lm.ravel()-np.real(tsfit2))\n",
    "print(np.max(aa))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "使用3个频率导致残差更接近白噪声过程。\n",
    "\n",
    "证明从傅里叶变换获得的参数值等效于时域线性回归模型。通过形成设计矩阵并求解法线方程，找到三个频率的总体均值、余弦幅度和正弦幅度的最小二乘估计值。将拟合时间序列与从傅里叶变换获得的时间序列进行比较。"
   ]
  }
 ],
 "metadata": {
  "interpreter": {
   "hash": "9ebf9cfd872009544a161647ac82c48f4cc096aba58631b69e515c7576d66293"
  },
  "kernelspec": {
   "display_name": "Python 3.6.13 ('pytorch')",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.13"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
